I also have both of them! And I've just check (fast checking) that pictures are absolutely same. Russian version contains small attachments (by Anosov), but they are not... as good as the book and really short, few pages. You know, translation should be a translation (I am sure Arnol'd could add smth interesting to Milnor, I am a student of V.I., but it is not the case).
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PetyaMar 11 '10 at 0:36

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At least I understood a meaning of your smile!
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PetyaMar 11 '10 at 0:49

51 Answers
51

There are two books on popular mathematics by Polish mathematicans Krzysztof Ciesielski and Zdzisław Pogoda (both from the Jagiellonian University in Krakow): the first one is Diamenty matematyki [Mathematical diamonds] (cover http://merlin.pl/images_big/3/83-7337-932-0.jpg), the second is Bezmiar matematycznej wyobraźni [The endlessness of mathematical imagination] (I could not find a better transaltion). Both aim at non-specialist, mostly high-school students, and are written in a unique, informal yet rigorous style. Both are very popular and out of print in Poland. A modified version of a chapter in Mathematical diamonds has been translated by Abe Shenitzer and was published in the American Mathematical Monthly as On Ordering the Natural Numbers, or, The Sharkovski Theorem in Vol. 115, No. 2 (Feb., 2008), pp. 159-165.

[Another answer contains this suggestion, but it's at the end of the answer and no details are given.]

I would rather like to read Kostrikin's Introduction to Algebra (the 2nd edition, published in 2000: Кострикин – Введение в алгебру). It is in 3 volumes: 'Basic algebra', 'Linear algebra', and 'Fundamental structures of algebra'. Approximately, they cover:

The book begins with a discussion about what algebra is, a historical overview, and a set of substantial problems that can be solved with algebra as motivation. Each volume contains a number of figures (67 in total), many applications, and a discussion of open problems (e.g. the convergence of Newton's method, finite projective planes, the inverse Galois problem).

From the Zentralblatt review: "The distinguishing features of the book are the following ones: 1) clearness, clarity and compactness of exposition; 2) the concentric style of presentation; 3) variety of skilfully selected examples (from very simple to very complex ones)."

[Note that the 1st edition was translated, but it is about a third as long and covers far less.]

B. P. Demidovich - Problems on Multivariate Analysis (approximate translation). A very tough book about analysis on $\mathbb{R}^n$; in fact all problems 'can' be solved by first or seond-year students, but it's got lots of tricky questions that will not let you sleep at night. Only the best need apply - the book gives you the most basic definitions and then throws you out with a broken pontoon in the middle of the ocean, at night. I believe the writer is Russian or Belorussian, I have only encountered a few tattered copies that have been doing the rounds between students for a decade at least. Haven't found a better book for tough multivariate analysis.

Paul Gordan ``Vorlesungen ueber Invariantentheorie"
available here , both volumes.
This is most worthwhile since the content of most other classics
is well accounted for in modern texts whereas this way of doing algebraic geometry has been completely forgotten. Poor knowledge of Gordan's methods is a net loss for contemporary mathematics.

Probably most of the works from Oskar Perron. It has been mentioned already Die Lehre von den Kettenbrüchen, both volumes, but we could also ask for Irrationalzahlen or any of the other works from Perron.
Also worth being mentioned, for applied mathematicians, are the works of Grigory Isaakovich Barenblatt, previous to 1994; this is because Barenblatt has consistently worked about scaling phenomena, but from about the beginnings of the 1990's he began to do it on his own, whereas earlier work includes the participation of other marvelous mathematicians, like Z'eldovich; or even works on his own, but it is interesting to compare the evolution of his ideas. So, the name of books with his participation previous to the 1990's, and to my knowledge, not translated into English:
* Ja, B Zeldovich, G. I. Barenblatt, V. B. Librovich, G. M. Maxvikadze "Matematicheskaja teorija gorenija i vsriva", 1980
* G. I. Barenblatt, "Podobie, avtomodelnoct, promezhutochnaja asimptotika: teorija i prilozhenija k geofizicheskoi gidrodinamike", 1982
* A. P. Licitsin, G. I. Barenblatt "gidrodinamika i osadkoobrasovanie", 1983
* G. I. Barenblatt, V. N. Entov, V. M. Rizhik, "Dvizhenie zhidkocteii i gazov v prirodnix plactax" 1984
* G. I. Barenblatt, "Analiz razmernosteii" . Uch. pos. M.: MFTI, 1987. 168 с. (I think this last work made it to English under the translation as "Dimensional Analysis", but in that case I saw it only once, at the library of the Department of Applied Mathematics and Theoretical Physics -DAMTP-of Cambridge, UK, many years ago and is likely out of print anyway, plus the edition, to my knowledge was not revised; on top of that, DAMTP changed from Silver Street to Wilberforce road, and I have no idea if that book survived the moving, if indeed was at that library).

Notice also, that in the Nachlass (the collection of manuscripts, left after the death of an academician, and of course in particular a mathematician) of people like Bernhard Riemann or Ernst Zermelo, there might be still some untranslated documents, but then again they also need to be interpreted in a way that could be meaningful, and this because they are not finished, published or even unpublished works, but sketches of something not fully developed.

F. Prus-Wisniowski - Szeregi Rzeczywiste (Poland, Uniwersytet Szczecinski) - a monograph on real series. It can be read by first-year students while supplying the reader with very powerful tools for real (and sometimes complex) series; it might surprise the PhD reader. More importantly, it builds a good understanding of the way real series work.
Publisher's website

Two volume introduction to Complex Analysis by B.V.Shabat. Actually, I have already translated about 150 pages of the first volume which is about as much as one can cover in Complex Variable undergraduate course offered by a typical U.S. university. I did give the translation as a hand out to my students last year when I taught Complex variables class. I did translation out of frustration with the book of Churchill and Brown.